split of adjoint solution

Hi Lyuda,

a) Adjoint solutions always live in the same function space as the original forward solutions. So the adjoint velocity-pressure lives in the MixedFunctionSpace for velocity-pressure, the adjoint temperature lives in the temperature function space, etc.

b) The adjoint solutions are computed in reverse order, i.e. from bottom to top in the HTML visualisation (which is dumped as adjoint.html).

c) Take a look at the adjoint computation loop:

  for (adjoint, var) in compute_adjoint(J, forget=False):
    pass

At the end of that loop, the variable "adjoint" will be the adjoint variable corresponding to whatever was the first variable in the annotation.

d) If you look at the annotation and dig around a bit, the first thing annotated is the initial condition for temperature. (This is far more obvious when you give things names, as I've done in the latest trunk, r446).

e) So, by the above, the "adjoint" variable at the end of that loop is the adjoint temperature, which lives in the temperature function space, and so cannot be split.

f) Now, if you want the adjoint solution for velocity-pressure (which I assume you do, since you're trying to split something), update to r446 and modify the loop to do the following:

   J = Functional(-(1.0/Nu2)*grad(Tfinal)[1]*ds2*dt[FINISH_TIME])
   for (adjoint, var) in compute_adjoint(J, forget=False):
- pass
+ if var.name == "InitialVelocity":
+ (adj_u, adj_p) = split(adjoint)

then adj_u and adj_p will be the adjoint velocity and pressure corresponding to the initial velocity guess computed in compute_initial_conditions.

Hope this helps!

Patrick